Making a flexible parameterized horn
Final:



Overview:

You will need two objects.


Simple Bezier Circle which will Bevel your shape.
Bezier Curved shaped as needed with custom Radius values (per point) for Beveling.




You can change Radius values by selecting point and changing it's value in Transform tab or by hitting W > Set Curve Radius.



After that you can add Solidify Modifier and maybe Alt+C > Mesh from Curve.

Blend file: